Function fitbsf for Bayesian Stochastic Frontier Analysis

Function fitbsf.m is easy to use and implements some well-known Bayesian Stochastic Frontier models.

# BSFAmk2

A simple to use function for Bayesian Stochastic Frontier Analysis

The main file to run is fitbsf.m which contains the named function.

Below is the description from fitbsf.m file on how to use it:

% Function for Bayesian estiamtion of several most popular Stochstic Frontier models.

%

% (c) 2020 Kamil Makiela

%

% Syntax:

% BSFA = fitbsf(x,y,name);

% BSFA = fitbsf(x,y,name,n);

% Description:

% BSFA = fitbsf(x,y,name) returns Bayesian fit of a Stochastic Frotnier

% production-oriented model, specified in 'name' using data in

% x (explanatory variables) and y (the dependent). In its simplest form

% the (logged) model is: y = intercept + x*beta + v - u; where u is the

% nonnegative component of inefficiency, so that r=exp(-u) is the

% standard efficiency measure known in SFA literature

% BSFA = fitbsf(x,y,name,n) returns Bayesian fit of an SF model for

% panel data (balanced panels only). Observations are to be stacked as

% object:time (not period:time!); see example below.

% inputs:

% x - explanatory variables in comlums (excluding column with "1"'s!!)

% y - the dependent; column vector

% NOTE: both y and x are assumed to have observations in logs of their

% original values so that there is a (log)linear dependency assumed

% bewteen x's and y

% name - name of SFA sampling model; you can choose from:

% nhn t - normal-half-normal with transient efficiency

% nhn p - normal-half-normal with persistent efficiency (needs "n")

% nex t - normal-exponential with transient efficiency

% nex p - normal-exponential with persistent efficiency

% nhn true - "true" random effects model (with transient [half

% normal] efficiency and a symmetric object sepcific effect (needs

% "n")

% nex true - "true" random effects model (with transient

% [exponential] efficiency and a symmetric object sepcific effect

% (needs "n")

% re - simple Bayesian random-effects model (non-SFA)

% n - (optional) number of objects (for panel data); it is assumed

% that observations are stacked in "object->time" order.

% output:

% BSFA - matlab structure with results:

% BSFA.coeffitients - posterior estimates and standard deviations of the

% function coefficients; the first coefficient is the intercept; the rest

% are in the order according to varaibles in matrics x

% BSFA.sigma_v - std of the symmetric disturbance

% BSFA.sigma_u - std of the inefficiency component

% BSFA.u - inefficiency estimates (or random effects in case of RE model)

% BSFA.ef - efficiency estimates

% BSFA.Loglikelihood - loglikelihood value of the Bayesian solution

% BSFA.model - name of the SFA model chosen

% BSFA.settings - simulation and model settings

% BSFA.sigma_a - (optional) std deviation of the additional symmetric

% object-specific disturbance (used in 'true' SFA models)

% BSFA.a - (optional) estimated random effects in 'true' SFA models for

% panel data

% ADDITIONAL options: see "function settings" section below

%

% Example

% estimating normal-half-normal SFA with persistent efficiency:

% ExampleData; % load example data

% bayes = fitbsf(x,y,'nhn p',n); % run selected SFA model

% output structure 'bayes' contains results

%

%% Function settings

beta_prior = 1; % if 1: informative prior on coefficients, uninformative otherwise

zapisz = 0; % if 1: saves gibbs cycles, results and settings to current directory

make_plots = 0; % if 1: displays sequential and cusum plots for the intercept

calc_came = 0; % if 1: the procedure also calculates the log of marginal data

% density (aka marignal likelihood) based on:

% corrected arithemtic mean estimator (Pajor, 2017; Bayesian Analysis)

% and harmonic mean estimator (Geweke, 1992)

% use informative prior setting (beta_prior=1) when

% using this option!

tot_cycles = 25000; % total number of cycles: in theory, the more the better (smaller numeric error)

burnin_cycles = 5000; % burnin phase; usually 10k is enough for most applications

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%